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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Cryptanalysis of the RSA Subgroup Assumption from TCC 2005
verfasst von : Jean-Sébastien Coron, Antoine Joux, Avradip Mandal, David Naccache, Mehdi Tibouchi
Erschienen in: Public Key Cryptography – PKC 2011
Verlag: Springer Berlin Heidelberg
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At TCC 2005, Groth underlined the usefulness of working in small RSA subgroups of hidden order. In assessing the security of the relevant hard problems, however, the best attack considered for a subgroup of size 2
2ℓ
had a complexity of
O
(2
ℓ
). Accordingly, ℓ= 100 bits was suggested as a concrete parameter.
This paper exhibits an attack with a complexity of roughly 2
ℓ/2
operations, suggesting that Groth’s original choice of parameters was overly aggressive. It also discusses the practicality of this new attack and various implementation issues.